Answer:
At least 401 chosen guests
Step-by-step explanation:
Represent those with same birth day with Same
So:
[tex]P(Same) > \frac{2}{3}[/tex]
Represent number of people with n
There are 365 days in a year and 364 days out of these days is not your birthday.
So, there the probability that n people do not share your birthday is [tex](\frac{364}{365})^n[/tex]
i.e.
[tex]P(none) = (\frac{364}{365})^n[/tex]
Solving further, we have that:
[tex]P(same) + P(none) = 1[/tex]
[tex]P(same) + (\frac{364}{365})^n = 1[/tex]
[tex]P(same) = 1 - (\frac{364}{365})^n[/tex]
We're calculating the probability that [tex]P(Same) > \frac{2}{3}[/tex].
So, we have:
[tex]1 - (\frac{364}{365})^n > \frac{2}{3}[/tex]
Collect Like Terms
[tex]1 - \frac{2}{3}> (\frac{364}{365})^n[/tex]
[tex]\frac{3-2}{3}> (\frac{364}{365})^n[/tex]
[tex]\frac{1}{3}> (\frac{364}{365})^n[/tex]
[tex]3^{-1} > (\frac{364}{365})^n[/tex]
Take natural logarithm (ln) of both sides
[tex]ln(3^{-1}) > ln((\frac{364}{365})^n)[/tex]
[tex]-ln\ 3 > n\ ln\ (\frac{364}{365})[/tex]
Apply laws of logarithm
[tex]-ln\ 3 > n\ (ln(364) - ln(365))[/tex]
Multiply through by -1
[tex]ln\ 3 < n\ (ln(365) - ln(364))[/tex]
Solve for n
[tex]\frac{ln\ 3}{(ln(365) - ln(364))} < n[/tex]
Reorder
[tex]n > \frac{ln\ 3}{(ln(365) - ln(364))}[/tex]
[tex]n > \frac{1.09861228867}{(5.89989735358 - 5.89715386764)}[/tex]
[tex]n> \frac{1.09861228867}{0.00274348594}[/tex]
[tex]n > 400.443928891[/tex]
[tex]n > 400[/tex] (approximated)
This implies that n = 401, 402, 403 .....
i.e
[tex]n \geq 401[/tex]
So, at least 401 people has to be invited
Aarti posted a comment on her blog. Each day the number of responses to her comment was 125% of the number she
received on the previous day. If there were 64 responses the first day, how many were there on the fourth day?
O 100
112
оооо
125
132
Mark this and return
Save and Exit
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Answer:
125
Step-by-step explanation:
Answer:
125
Step-by-step explanation:
the ratio of the angles in a triangle is 3:10:7, what is the measure of the smallest angle
Answer:
27°
Step-by-step explanation:
Let the measure of the angels be 3x, 10x, 7x.
[tex]3x + 10x + 7x = 180 \degree \\ \\ 20x = 180 \degree \\ \\ x = \frac{180 \degree}{20} \\ \\ x = 9 \degree \\ smallest \: angle \: = 3x \\ \\ = 3 \times 9 \degree \\ \\ = 27 \degree[/tex]
4.5.36
A smoke jumper jumps from a plane that is 1500 ft above the ground. The function h= -16? + 1500 gives the jumper's height hin feet during the free fall att seconds
a. How long is the jumper in free fall if the parachute opens at 1000 ft?
b. How long is the jumper in free fall if the parachute opens at 940 ft?
c. What is a reasonable domain and range for the function h? no
Answer:
Step-by-step explanation:
Given function is h(t) = -16t² + 1500
a). For h(t) = 1000 feet,
1000 = -16t² + 1500
1000 - 1500 = -16t² + 1500 - 1500
-500 = -16t²
t² = [tex]\frac{500}{16}[/tex]
t = [tex]\sqrt{31.25}[/tex]
t = 5.59 sec
b). For h(t) = 940 feet,
940 = -16t² + 1500
940 - 1500 = -16t² + 1500 - 1500
-16t² = -560
t² = [tex]\frac{-560}{-16}[/tex]
t = [tex]\sqrt{35}[/tex]
t = 5.92 sec
c). For domain and range of the function,
When the jumper comes down to the ground,
h = 0
0 =-16t² + 1500
t² = [tex]\frac{1500}{16}[/tex]
t = [tex]\sqrt{93.75}[/tex]
t = 9.68 sec
Since, x-values on the graph vary from x = 0 to x = 9.68,
Domain : [0, 9.68]
Vertex of the quadratic function: (0, 1500)
Since, coefficient of the highest degree term is negative, parabola will open downwards.
Therefore, y-values of the function will vary in the interval y = 0 to y = 1500
Range: [0, 1500]
What is the hourly utilization rate of each resource if the bottleneck(s) work nonstop during a 10-hour day?
Answer:
100%
Step-by-step explanation:
Utilization rate =
Hours worked / total working hours per day
Since the bottle works nonstop during a 10-hour day, it worked 10 hours
Utilization rate in percentage = (10/10)×100%
= 100%
A certain plant grows 1 1/6 inches every week. How long will it take the plant to grow 4 1/6 inches?
Answer:
3 weeks and 4 days.
Step-by-step explanation:
If the plant grows 1 1/6 inches every week, then that means 1/6 inch everyday. 1 1/6 x 3 = 3 3/6
3 3/6 + (1/6 x 4) = 4 1/6
3 weeks and 4 days
Help?!
I dont understand this Help?!
1. 8x^2 + 10x - 9
2. 3x^4 - 14x^2 - 9
3. 4x^2 + 5x - 9
4. 8x^2 + 10x - 18
Answer:
4.
Step-by-step explanation:
(x^2 + 7x - 9) + (3x^2 - 2x) + (x^2 + 7x - 9) + (3x^2 - 2x)
x^2 + 7x - 9 + 3x^2 - 2x + x^2 + 7x - 9 + 3x^2 - 2x
Rearranging order:
3x^2 + 3x^2 + x^2 + x^2 + 7x + 7x - 2x - 2x - 9 - 9
Combine like terms
8x^2 + 10x - 18
What is on way feudal japan was different than feudal Europe???? Not mathematics it is history.
the term to term rule of a sequence is divide by 2
If f(1) = 6 and f(n) = f(n-1) + 2 then find the value of f(4).
Answer:
5
Step-by-step explanation:
f(4-1)+2
=3+2
=5
PLS GIVE BRAINLIEST
help asap. will give best answer.
Answer:
neither
Step-by-step explanation:
Instead of handing out candy like a well-adjusted person on Halloween, grumpy, anti-social Professor Sosa decides to stand on top of a 400 ft building and toss candy treats onto the ground below. If he drops a bag of candy corn, how long will it take for it to land on the ground? What will the velocity of the bag be when it hits the ground?
Answer: The bag of candy corn will take 5 seconds to land on the floor and it will hit it with velocity of 49m/s.
Step-by-step explanation: A free falling object has only Gravitational Force acting on it, so acceleration will be due to gravity, which has magnitude
g = 9.8m/s².
As Professor Sosa drops the bag, its initial velocity and time are 0.
The building has a height of 400ft, so adjusting units: y = 121.92 m and [tex]y_{0}[/tex] = 0.
For this problem, going down will be the positive reference.
Then:
[tex]y=y_{0}+v_{0}t+\frac{g}{2}t^{2}[/tex]
[tex]\Delta y=v_{0}t+\frac{g}{2}t^{2}[/tex]
[tex]121.92=\frac{9.8}{2}t^{2}[/tex]
[tex]t=\sqrt{\frac{121.92*2}{9.8} }[/tex]
t ≈ 5
It will take 5s for the candy corn bag to land on the ground.
Acceleration is the change in velocity per change in time, so:
[tex]g=\frac{\Delta v}{\Delta t}[/tex]
As initial velocity and time are 0 and rearraging it:
v = g.t
v = 9.8*5
v = 49
The bag will hit the ground with velocity of magnitude 49 m/s.
Solve the quadratic equation.
3x^2-12=16x
Answer:
I think the answer is
x = 6, -2/3
Step-by-step explanation:
I hope this helps please let me know if it is incorrect
the ratio 60 miles per hour is an example of a ______because it has two measurements having different units of measure
Answers:
1.Annex
2.Rate
3.Unit rate
4.Least common multiple
Answer:
3. Unit Rate
Step-by-step explanation:
The answer is Unit Rate because it is describing two units of measurements compared to one another.
please help!! find the reciprocal of these numbers.
6.2
-2.3
0.9
-22.7
Answer:
They have its own reciprocal
Write (6*100) + (4*10) in standard form
HELP PLEASE I’ll make you brilliant
Answer:
this is grade what????
Step-by-step explanation:
Every 125 pages that Raul reads during his summer reading challenge, he will collect 5 book points to use at his local library. Which graph models a relationship with the same unit rate?
Answer:
d. J
Step-by-step explanation:
Given that Raul gets 5 (y) book points for every 125 (x) pages he reads during summer challenge, we can say that his unit rate would be: y/x = 5/125 = 1/25.
Raul's unit rate is 1/25 book point to each page he reads.
Graph J also has a unit rate of 1/25 (y/x).
Therefore graph J models a relationship with the same unit rate.
What is 40x52 To the 7 power
Answer:
168,439,267,742,187,520,000,000
Step-by-step explanation:
40*52=2080
2080^7=168,439,267,742,187,520,000,000
Select the more effective use of correlative conjunctions to join these sentences.
The manager of the supermarket will help the new employee. The assistant manager may help the employee, too.
A. Neither the manager of the supermarket nor the assistant manager may help the new employee.
B. Both the manager of the supermarket and the assistant manager may help the new employee.
hurry .
Answer:
b the answer
Step-by-step explanation:
Answer:
Answer is B
Step-by-step explanation:
Alex rents a car for one day. The charge is $18 plus $0.12 per mile. Alex wants to spend exactly $30. How many miles can he drive.
Answer:
Alex can drive for 100 miles.
Step-by-step explanation:
First, you do 30 - 18, which is 12. Divide 12 by 0.12 to get your answer, which is 100 miles.
Hope this answer helped!
Answer:
Alex can drive for 100 miles
Step-by-step explanation:
Estimate 9146 x 174 by first rounding each number so that it has only 1 nonzero digit.
Answer:
1,800,000
Step-by-step explanation:
9146 * 174
Estimate: 9000 * 200 = 1,800,000
Based on simple interest, how much money would you have borrowed at 6% annual interest if your interest payment for one year was $120?
7-99 Find the missing information in each set of equivalent ratios below, using any method. Be
sure that you record your process so that others can see what you did.
2
15
100
Noo
100
Work for A
37.5
I
Work for B
87.5
0.2
2
х
11.2
Answer:
21 man
Step-by-step explanation:
u have to do the work and get the answer
The table below shows the total number of hours Jessica,Emily,and Trina each studied after a given number of weeks
Answer:
See attached
Step-by-step explanation:
Refer to attached
Only column 3 - Trina's numbers represents proportional relationship
Equation for it is:
y = 2.5xCalculation is provided on the table
PLZZZZZZZZZZZZZZZZZZZZZZ HELP!!!
QUESTION: -2(x-6)=8
STUDENT WORK:
-2(x-6)=8
-2x-12=8
-12 -12
-2x+0=-4
-2x=-4
÷2 ÷2
x=-2
1. Explanation of Errors Made
2. Correct Solution (show all work)
Answer:
The error was made in the division step it should have been divided by negative 2
-2(x-6)=8
-2x+12=8
-2x=-4
-x=-2
X=2
What is the area, in square inches, of this kite?
7 in.
5 in.
5 in.
10 in
(pls help)
Step-by-step explanation:
I think its 85in as the area.
Which of the expressions are equivalent to the one below? Check all that
apply.
16. (1 + 3)
A. (16. 1) + (3.16)
B. (3 + 1). 16
D C. (16 + 3). 1
D. (161) + (163)
so A & B = 64 .... so yeah right A & B are the correct answers
by the way i multiplied for the "."
pls pls pls help i am terrible at math.
where do the points go?
Answer:
I presume that 10x would be on the x axis to the right of 0.
-7y would be on the y axis under 0. Therefore in between -6 and -8
You might know this but very important
X to the decks (horizontally/straight across) and Y to the sky (vertically/ up and down)
^DEF and ^RSQ are shown in the diagram below
Based on the information provided in the diagram, what is mZQ in degrees?
Answer:
53.3 degrees
Step-by-step explanation:
∆DEF and ∆RSQ are similar. We know this, because the ratio of their corresponding sides are equal. That is:
DE corresponds to RS
EF corresponds to SQ
DF corresponds to RQ.
Also <D corresponds to <R, <E corresponds to <S, and <F corresponds to <Q.
The ratio of their corresponding sides = DE/RS = 6/3 = 2
EG/SQ = 8/4 = 2
DF/RQ = 4/2 = 2.
Since the ratio of their corresponding sides are equal, it means ∆DEF and ∆RSQ are similar.
Therefore, their corresponding angles would be equal.
Thus, m<Q = m<F
Let's find angle F
m<F = 180 - (98 + 28.7)
m<F = 53.3°
Since <F corresponds to <Q, therefore,
m<Q = 53.3°